Yes, you can run normal (flex), heroic (normal) and mythic (heroic) every week (in addition to LFR, of course, if you're really sadistic). With the flex modes (normal and heroic) moving to group loot, I highly doubt you will be able to participate in multiple lockouts of those modes each week. They would have to come up with a way of blocking you from receiving loot after the first kill, and I think it would prove highly unpopular.
This also seems to mean you will not be able to skip mythic bosses to get to easier ones later in linear instances, as you cannot apply your heroic kills to your mythic lockout.
Any of this is obviously subject to change, but this is what they seem to be attempting to do for now.
LFR, Normal and Heroic will work like LFR/Flex works now. That is to say you can do all of them in the same week. You can also kill the same boss multiple times that week, but you only get loot from the bosses one time per week, per difficulty. If I understand it correctly Mythic will not work the same though. You only get to kill each boss in Mythic one time per week.